Compensation of reflective mask effects in lithography systems

ABSTRACT

Aberrations may be introduced in mirror surfaces used in a lithography system utilizing a reflective mask to compensate for adverse optical effects associated with reflective masks. A spherical aberration may be introduced to compensate for a shift in the location of best focus. A coma aberration may be introduced to compensate for a pattern shift.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional application of and claims priority toU.S. patent application Ser. No. 10/366,583, filed Feb. 12, 2003 nowU.S. Pat. No. 7,022,443.

BACKGROUND

Many lithography systems use transmissive masks to image a pattern on awafer. Light which passes through transparent portions of the mask mayform a pattern on a photoresist material on the mask. Lithographysystems may also use reflective masks to image a pattern on a wafer.Light may be reflected off of a reflective mask rather than passingthrough the mask, as with a transmissive mask.

Light may be directed to a reflective mask at an incident angle offnormal. Due to this angle of incidence, features parallel to the planeof incidence (e.g., horizontal features) may exhibit a shadowing effect.Features parallel to the plane of incidence (e.g., vertical features)may not exhibit the shadowing effect.

The difference in shadowing effect between the horizontal and verticalfeatures may make the horizontal features projected onto the imagingplane larger than the vertical features. To compensate for this effect,the horizontal features may be drawn on the mask such that they arescaled smaller than the vertical features.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an extreme ultraviolet (EUV) lithographysystem.

FIG. 2 is a plot showing the Bossung curves for a 30 nm line with 160 nmpitch on a thick mask with zero degree tilt.

FIG. 3 is a plot showing the location of best focus for 30 nm linesthrough pitch at zero degrees and six degrees of tilt.

FIG. 4 is a plot showing the impact of primary, secondary, and tertiaryspherical aberrations on the location of best focus for semi-isolated 30nm lines.

FIG. 5 is a plot showing the effect of introducing a sphericalaberration on the location of best focus for 30 nm lines at zero degreesand six degrees of tilt.

FIG. 6 is a side view of a reflective mask illuminated with radiation atan angle of incidence.

FIG. 7 is a plot showing the relationship between center shift andincident angle.

FIG. 8 is a plot showing the effect of introducing a coma aberration oncenter shift.

DETAILED DESCRIPTION

FIG. 1 illustrates a lithography system 100. In an embodiment, thelithography system may be an Extreme Ultraviolet (EUV) lithographysystem. EUV lithography is a projection lithography technique which mayuse a reduction optical system and illumination in the soft X-rayspectrum (e.g., wavelengths in the range of about 10 nm to 20 nm).

The system 100 may include a source 105 of EUV radiation 110, imagingcollectors 115, a pupil 120, condenser optics 125, a reticle mask 130,and an optical system including four high precision mirrors 135-138. Theoptical elements in the system (e.g., the imaging collectors 115, pupil110, condenser 125, and mirrors 135-138) may be mirrors made to bereflective to EUV light of a particular wavelength (typically 13.4 nm)by means of multilayer coatings, e.g., alternating layers of molybdenumand silicon (Mo/Si) or molybdenum and beryllium (Mo/Be). The alternatinglayers may produce constructive interference in the direction ofreflection. Since EUV is strongly absorbed by materials and gases, thelithography process may be carried out in a vacuum, and a reflective,rather than transmissive, reticle mask 130 may be used.

The source 105 of soft X-rays may be a compact high-average-power,high-repetition-rate laser which impacts a target material to producebroad band radiation with significant EUV emission. The target materialmay be, for example, a plasma generated from a noble gas, such as Xenon(Xe). The target material may convert a portion of the laser energy intoEUV radiation with an energy of about 90 eV to 100 eV.

The condenser optics 125 may collect EUV light from the source andcondition the light to uniformly illuminate the mask 130 and properlyfill the pupil 110. The condenser optics may include a series ofaspheric mirrors, which collect the radiation and reflect it at a lowangle.

The radiation from the condenser optics may be directed to the mask 130.The mask may include a multiple-layer reflecting substrate with apatterned, absorbing overlayer. The reflected EUV radiation from themask 130 may carry an integrated circuit (IC) pattern on the mask 130 toa photoresist layer on a wafer 140 via the optical system includingmultilayer mirrors 135-138. The entire reticle may be exposed onto thewafer 140 by synchronously scanning the mask and the wafer, e.g., by astep-and-scan exposure.

The center of best focus in a lithographic imaging operation may ideallybe at zero defocus. However, the use of reflective masks in EUVLithography has been shown to introduce a shift in the location of bestfocus that varies as a function of feature size and pitch.

The shift in the location of best focus for reflective masks in EUVlithography may be due to the skewed shape of the Bossung curves (CD vs.focus and exposure). FIG. 2 shows the Bossung curves 200 for a 30 nmline with 160 nm pitch on a thick mask with zero degree tilt. Thelocation of best focus 210 in this case has shifted to the right, suchthat the Bossung curves are not symmetric about zero defocus 215. Thelocation of best focus is not at zero defocus but at about 0.04 μm (40nm).

FIG. 3 shows the location of best focus for 30 nm lines at zero degrees305 and six degrees 305 of tilt. The depth of focus of 30 nm isolatedlines in a typical EUV lithography system may be about 150 nm to 200 nm.The difference in the location of best focus between isolated lines andnested lines in this range may be as high as 30 nm, which may reduce theoverall process window by about 20%.

A shift in the location of best focus may also be caused by aberrationsin a lens. In an embodiment, selective aberrations may be introducedinto one or more mirror surfaces in the lithography system to compensatefor the shift in best focus inherent to reflective masks.

In a lens system, lens aberrations result in a deviation of thewavefront from the ideal. The aberration of a ray may be denoted by fivesums called the Siedel sums. Each of these sums denotes a contributionfrom a classical form of monochromatic aberration. The monochromaticaberrations include spherical, coma, astigmatism, curvature, anddistortion aberrations.

Spherical aberrations may be due to different annular zones in the lenshaving different focal lengths. The effect of coma is similar tospherical aberrations except that coma affects object points that arenot on the optic axis. Coma changes the image to look like a comet,hence the name. Coma arises where different annular zones of the lenshave different magnifications so that portions of an off-axis imagecontributed by particular zones are displaced from the optical axis byvarying amounts. Astigmatism is similar to coma in that it impactsobject points that are not on the optic axis. However, in astigmatismthe spreading of the image takes place along the lens axis. This is dueto the focal lengths being different for rays along mutually orthogonalplanes. Field curvature is an image defect that causes off-axis imagepoints to focus in different focal planes than the axial image point.The variation in the magnification produced by a lens for differentaxial distances results in an aberration called distortion.

The deviation of the real spherical wavefront from the ideal in the exitpupil due to these aberrations may be quantified by an optical path (orphase) difference Δ(ρ, θ), where (ρ, θ) are the co-ordinates in the exitpupil.

Zernike polynomials may be used to represent aberrations in diffractionoptics. Aberrations described by the Zernike polynomials include theclassical Seidel aberrations described above, but also capture higherorders of aberrations.

Zernike polynomials are one of an infinite number of complete sets ofpolynomials in two real variables, ρ and θ, which are orthogonal in acontinuous fashion over the interior of a unit circle. Zernikepolynomials are orthogonal only in a continuous fashion over theinterior of a unit circle, and in general they will not be orthogonalover a discrete set of data points within a unit circle.

A list of the thirty-seven Zernike polynomial coefficients that make upthe aberrations is given in Table 1. The set of thirty-seven polynomialcoefficients applies to only one location of the lens. So, if adescription of the effect of aberrations such as horizontal/vertical(H/V) delta across n slot positions is required, then n sets of Zernikepolynomial coefficients are needed.

SVG Zernike Formula  Z1 1 Piston or Bias: No change  Z2 2ρ cos θ x-tilt:Shifts pattern without distortion  z3 2ρ sin θ y-tilt  z4 √3 (2ρ² − 1)Defocus: Similar to Siedel field curvature  z5 √6 ρ²cos 2θ H/Vastigmatism: gives H-V delta CD  z6 √6 ρ²sin 2θ astigmatism 45°  z7 √8(3ρ³ − 2ρ)cos θ primary y-coma: Results in image asymmetry and patterndependent position shift  z8 √8 (3ρ³ − 2ρ) sin θ Primary x-coma  z9 √8ρ³ cos 3θ Higher order tilt & image anomalies with threefold symmetryz10 √8 ρ³ sin 3θ Higher order tilt 3 leaf clover z11 √5 (6ρ⁴ − 6ρ² + 1)Primary spherical z12 √10 (4ρ⁴ − 3ρ²) cos 2θ Secondary astigmatism z13√10 (4ρ⁴ − 3ρ²) sin 2θ z14 √10 ρ⁴ cos 4θ z15 √10 ρ⁴ sin 4θ z16 √12 (10ρ⁵− 12ρ³ + 3ρ) cos θ Secondary y-coma z17 √12 (10ρ⁵ − 12ρ³ + 3ρ) sin θSecondary x-coma z18 √12 (5ρ⁵ − 4ρ³) cos 3θ z19 √12 (5ρ⁵ − 4ρ³) sin 3θz20 √12 ρ⁵ cos 5θ z21 √12 ρ⁵ sin 5θ z22 √7 (20ρ⁶ − 30ρ⁴ + 12ρ²− 1)Secondary spherical z23 √14 (15ρ⁶ − 20ρ⁴ + 6ρ²) cos 2θ z24 √14 (15ρ⁶ −20ρ⁴ + 6ρ²) sin 2θ z25 √14 (6ρ⁶ − 5ρ⁴) cos 4θ z26 √14 (6ρ⁶ − 5ρ⁴) sin 4θz27 √14 ρ⁶ cos 6θ z28 √14 ρ⁶ sin 6θ z29 4(35ρ⁷ − 60ρ⁵ + 30ρ³− 4ρ) cos θTertiary y-coma z30 4(35ρ⁷ − 60ρ⁵ + 30ρ³− 4ρ) sin θ Tertiary x-coma z314(21ρ⁷ − 30ρ⁵ + 10ρ³) cos 3θ z32 4(21ρ⁷ − 30ρ⁵ + 10ρ³) sin 3θ z33 4(7ρ⁷− 6ρ⁵) cos 5θ z34 4(7ρ⁷ − 6ρ⁵) sin 5θ z35 4ρ⁷ cos 7θ z36 4ρ⁷ sin 7θ z373 (70ρ⁸ − 140ρ⁶ + 90ρ⁴ − 20ρ² + 1) Tertiary spherical

Table 1: Zernike Polynomials

The Zernike aberrations are made up of one or more classical Siedelaberrations. The classical aberration of the highest degree in pupilcoordinates may be optimally balanced with those of equal and lowerdegrees such that its variance across the pupil is minimized. Forexample, the Z11 polynomial 1 consists of the primary sphericalaberration ρ⁴ optimally balanced with a ρ² defocus term to minimize itsvariance.

FIG. 4 shows the impact of primary 405, secondary 410, and tertiary 415spherical aberrations (Z11, Z22, and Z37, respectively) on the locationof best focus for semi-isolated 30 nm lines. It can be seen that Z11 hasthe largest impact, and the change in the direction of best focus (intoor away from the wafer plane) depends on the sign of the sphericalaberration (i.e., positive or negative).

In an embodiment, small amounts of primary spherical aberrations (Z11)may be introduced into a mirror surface in the lithography system 100 tocompensate for the shift in location of best focus inherent toreflective masks. For most pitches, the best focus range is reduced toabout 10 nm, as shown in FIG. 5, as opposed to 30 nm for the case of noaberrations. This corresponds to about a 300% improvement in thelocation of best focus.

Aberrations may be introduced on a mirror surface by selective polishingof the surface. For example, QED Technologies of Rochester, N.Y.produces computer-controlled polishing tools which may be used tointroduce aberrations into an optical surface. The polishing tool mayuse a “controllable” fluid, e.g., a fluid with magnetorheological (MR)properties, to polish optical surfaces. The tool may use an algorithmwhich determines the local polish rate to produce a desired surfacegeometry. The tool may enable a user to create a surface topography on amirror based on a mathematical description. For example, the topographyof a spherical aberration (Z11) may be described by the equation1−6(x²+y²)+6(x²+y²)². Using this formula, the computer-controlledpolishing tool may generate the required surface topography to give thedesired level of a spherical aberration (Z11) on the mirror surface.

Another optical effect associated with reflective masks is pattern shiftdue to a shadowing effect. As shown in FIG. 6, light 605 may be directedto the reflective mask at an incident angle 610 from normal 615. Theangle of incidence may be, e.g., about 6 degrees from normal. Due tothis angle of incidence, features 620 parallel to the plane of incidence(e.g., horizontal features) may exhibit a shadowing effect. Featuresparallel to the plane of incidence (e.g., vertical features) may notexhibit the shadowing effect.

As shown in FIG. 7, the larger the incident angle the greater thepattern shift. For 30 nm features that are oriented perpendicular to theplane of incidence of the light at the reticle (at 6° off-normal), thepattern shift 705 may be about 5 nm. However, the alignment budget forthe lithographic imaging operation may only be about 15 nm. This patternshift needs to be compensated for to prevent alignment problems betweenfeatures on the mask. Misalignments may lead to imbalances in the IC,which could result in anomalous circuit behavior, or in extreme cases,critical defects such as shorts.

A coma aberration on a lens may also cause such a pattern shift. In anembodiment, the pattern shift due to the shadowing effect may becompensated by introducing small amounts of coma aberration.

FIG. 8 shows the center shift 800 due to Z8 (primary y-coma) aberration.A coma aberration amount of +0.04 waves that results in a −4 nm shift805 may compensate for +4 nm shift that occurs due to a 5° angle ofincidence. The topography of a coma aberration (Z8) may be described bythe equation 7x(−2+3(x²+y²) ). The coma aberration may be introducedinto a mirror surface in the lithographic system using acomputer-controlled polishing tool, as describe above.

A number of embodiments have been described. Nevertheless, it will beunderstood that various modifications may be made without departing fromthe spirit and scope of the invention. Accordingly, other embodimentsare within the scope of the following claims.

1. An apparatus comprising: an optical path including an image plane, areflective reticle mask operative to cause different shifts inlocations, at the image plane, of best focus of features havingdifferent sizes or pitches, and a reflective surface including aspherical aberration operative to compensate for the shifts in thelocations of best focus.
 2. The apparatus of claim 1, wherein thespherical aberration is operative to shift the locations of best focusof the features towards zero defocus.
 3. The apparatus of claim 1,wherein the spherical aberration comprises a Z11 spherical aberration.4. The apparatus of claim 1, wherein the spherical aberration isoperative to reduce a range of the shifts in the locations of best focusto about 10 nm or less.
 5. The apparatus of claim 1, wherein thereflective surface comprises a surface of a single mirror in the opticalpath.
 6. The apparatus of claim 5, wherein the reflective surfaceincludes Z11, Z22, or Z37 spherical aberration operative to reduce arange of the different shifts in the locations of best focus to about 10nm or less in an image plane.
 7. The apparatus of claim 1, wherein thereflective surface comprises surfaces of multiple mirrors in the opticalpath.
 8. An apparatus comprising: an optical path including an imageplane, a reflective reticle mask operative to cause different patternshifts of features disposed at different angles of incidence withrespect to the optical path, and a reflective surface including a comaaberration operative to compensate for the pattern shifts of thefeatures disposed at the different angles of incidence.
 9. The apparatusof claim 8, wherein the coma aberration is operative to cause patternshifts in a direction opposite to a direction of the pattern shiftscaused by the reflective reticle mask.
 10. The apparatus of claim 8,wherein the coma aberration comprises a Z8 coma aberration.
 11. Theapparatus of claim 8, wherein the coma aberration is operative to causepattern shifts having a magnitude approximately equal to a magnitude ofthe pattern shifts caused by the reflective reticle mask.
 12. Theapparatus of claim 8, wherein the coma aberration is operative to shifta pattern of a feature by about 4 nm or greater.
 13. The apparatus ofclaim 8, wherein the reflective surface comprises a surface of a singlemirror in the path.
 14. The apparatus of claim 8, wherein the reflectivesurface comprises surfaces of multiple mirrors in the optical path. 15.An apparatus comprising: a mirror reflective to soft X-rayelectromagnetic radiation suitable for lithography, wherein the mirrorcomprises a reflective surface including Z11, Z22, or Z37 sphericalaberration operative to compensate for at least a portion of differentshifts in location of best focus of different features of a reticlemask, wherein the different features have different sizes or pitches.16. An apparatus comprising: a mirror reflective to soft X-rayelectromagnetic radiation suitable for lithography, wherein the mirrorcomprises a reflective surface including coma aberration operative tocompensate for at least a portion of different pattern shifts ofdifferent features of a reticle mask, wherein the different features areto be disposed at different angles of incidence with respect to anoptical path in a lithography system.
 17. The apparatus of claim 16,wherein the reflective surface includes Z8 (primary y-coma) aberration.